Mathematics in Natural Sciences and Arts Flashcards
A pattern has symmetry if there is an ____ of the plane that preserves the pattern
isometry
process which shifts points of the plane to possibly new locations in the plane
Transformation
types of transformation
Translation, Reflection, Rotation, Dilation
mapping that preserves distance (and therefore shape)
Isometry of the plane
Four types of plane isometries
Translation
Reflection
Rotation
Glide reflection
moves a shape in a given direction by sliding it up, down, sideways, or diagonally.
translation
can be thought of as getting a mirror image.
reflection
has a point about which the rotation is made and an angle that says how far to rotate.
rotation
is a transformation which changes the size of an object.
dilation
transformations which leave the dimensions of the object and its image unchanged
Isometries
transformations which leave the dimensions of the object and its image unchanged
is a combination of two transformations: a reflection and a translation.
Glide Reflection
figure with at least one non-trivial symmetry.
design
design that has a translation symmetry
pattern
has symmetry if there is an isometry of the plane that preserves it
plane pattern
TYPES OF SYMMETRIC PATTERNS
ROSETTE PATTERN
FRIEZE PATTERN
WALLPAPER PATTERN
finite groups of isometries which can contain just rotations and reflections
Rosette patterns
Two types of rosette patterns
Cyclic rosettes
Dihedral rosettes
has n-fold rotational symmetry and no reflectional symmetry
Cyclic rosettes
has n-fold rotational symmetry and reflectional symmetry
Dihedral rosettes